Related papers: Learning Mixtures of Gaussians Using the DDPM Obje…

By learning the gradient of smoothed data distributions, diffusion models can iteratively generate samples from complex distributions. The learned score function enables their generalization capabilities, but how the learned score relates…

This paper studies the original discrete-time denoising diffusion probabilistic model (DDPM) from a probabilistic point of view. We present three main theoretical results. First, we show that the time-dependent score function associated…

Diffusion models have emerged as a popular family of deep generative models (DGMs). In the literature, it has been claimed that one class of diffusion models -- denoising diffusion probabilistic models (DDPMs) -- demonstrate superior image…

Diffusion models achieve state-of-the-art performance in various generation tasks. However, their theoretical foundations fall far behind. This paper studies score approximation, estimation, and distribution recovery of diffusion models,…

Denoising diffusion models (DDMs) offer a flexible framework for sampling from high dimensional data distributions. DDMs generate a path of probability distributions interpolating between a reference Gaussian distribution and a data…

Remote sensing change detection is crucial for understanding the dynamics of our planet's surface, facilitating the monitoring of environmental changes, evaluating human impact, predicting future trends, and supporting decision-making. In…

Denoising diffusion models have become ubiquitous for generative modeling. The core idea is to transport the data distribution to a Gaussian by using a diffusion. Approximate samples from the data distribution are then obtained by…

Denoising Diffusion Probabilistic Models (DDPMs) have achieved impressive performance on various generation tasks. By modeling the reverse process of gradually diffusing the data distribution into a Gaussian distribution, generating a…

We provide new convergence guarantees in Wasserstein distance for diffusion-based generative models, covering both stochastic (DDPM-like) and deterministic (DDIM-like) sampling methods. We introduce a simple framework to analyze…

Practical diffusion sampling is a numerical approximation problem: under a fixed inference budget, one must simulate a reverse-time ODE or SDE using only a limited number of denoising steps, so discretization error is often the dominant…

Score-based diffusion models have achieved remarkable empirical success in generating high-quality samples from target data distributions. Among them, the Denoising Diffusion Probabilistic Model (DDPM) is one of the most widely used…

Out-of-distribution detection is crucial to the safe deployment of machine learning systems. Currently, unsupervised out-of-distribution detection is dominated by generative-based approaches that make use of estimates of the likelihood or…

Understanding causal dependencies in observational data is critical for informing decision-making. These relationships are often modeled as Bayesian Networks (BNs) and Directed Acyclic Graphs (DAGs). Existing methods, such as NOTEARS and…

Digital Surface Models (DSM) offer a wealth of height information for understanding the Earth's surface as well as monitoring the existence or change in natural and man-made structures. Classical height estimation requires multi-view…

Discrete diffusion models (DDMs) are a powerful class of generative models for categorical data, but they typically require many function evaluations for a single sample, making inference expensive. Existing acceleration methods either rely…

Nowadays, denoising diffusion probabilistic models have been adapted for many image segmentation tasks. However, existing end-to-end models have already demonstrated remarkable capabilities. Rather than using denoising diffusion…

Mixtures of Gaussian (or normal) distributions arise in a variety of application areas. Many heuristics have been proposed for the task of finding the component Gaussians given samples from the mixture, such as the EM algorithm, a…

We investigate the approximation efficiency of score functions by deep neural networks in diffusion-based generative modeling. While existing approximation theories utilize the smoothness of score functions, they suffer from the curse of…

Diffusion models have emerged as a dominant framework for generative modeling, but their mathematical foundations are often presented separately through diffusion probabilistic models, score-based modeling, stochastic differential…

Stochastic gradient descent (SGD) is widely used in deep learning due to its computational efficiency, but a complete understanding of why SGD performs so well remains a major challenge. It has been observed empirically that most…